Mahler measure and its behavior under iteration

For an algebraic number $\alpha$ we denote by $M(\alpha)$ the Mahler measure of $\alpha$. Mahler measure is a height function on polynomials with integer coefficients. Moreover, as $M(\alpha)$ is again an algebraic number (indeed, an algebraic integer), $M(\cdot)$ is a self-map on $\mathbb{A}$(Sometimes denoted $\overline{\mathbb{Q}}$), and therefore defines a dynamical system. The \emph{orbit size} of $\alpha$, denoted $\# \mathcal{O}_M(\alpha)$, is the cardinality of the forward orbit of $\alpha$ under $M$. In this thesis, we will start by introducing the background of Mahler measure as a height and a dynamical system, we will review previous results on the orbit sizes of lower degree algebraic integers and lower degree number fields, then we discuss results on the orbit sizes of algebraic integers with degree at least 3 and non-unit norm. After that, we will turn our focus to the behavior of algebraic units, which are of interest in Lehmer's problem. We will prove the results regarding algebraic units of degree 4 and discuss that if $\alpha$ is an algebraic unit of degree $d\geq 5$ such that the Galois group of the Galois closure of $\mathbb{Q}(\alpha)$ contains $A_d$, then the orbit size must be 1, 2 or $\infty$. Furthermore, we will show that there exist units with orbit sizes larger than 2. We will also show a few experimental results on the behavior of $(\log(M^{n}(\alpha)))$. In chapter five, we will prove partial results on the classification of number fields based on the existence of wandering points

The Impacts of China’s ETS on Firm Competitiveness; Evidence from the Power and Heat Production Sector

Carbon emissions are one of the primary causes of climate change. In the coming decades, the economic costs to deal with climate change are estimated to be 10% of the global GDP. To mitigate the threats, Emission Trading Scheme (ETS) is proposed as a cost-efficient carbon pricing approach to reduce the CO2 emissions in industrial production. Since 2013, the Chinese government has launched seven pilot ETS projects, and successionally, in 2021, the national carbon trading market was established. The national ETS in China covers more than 2,000 power and heat production plants, which accounts for 40% to 50% of China's industrial emissions and 10% of worldwide carbon emissions. Even though the expansion of China ETS is rapid, there is a limited number of analyses on the effectiveness and impacts of ETS. This study aims to further the understanding of the impacts of China’s pilot Emission Trading Scheme (ETS) on firm competitiveness in the power and heat production sector. According to the market externality of environmental emissions and Resource Dependency Theory (RDT), the pilot ETS will inevitably affect the firms’ production and introduce uncertainties to their decision-making process. However, there has been no consensus for debates between the Compliance Cost Hypothesis and the Porter Hypothesis over the impact of environmental regulations on firms. Maintaining firms’ competitiveness in the sluggish market is critical after the COVID pandemic. Firms with better competitiveness are more attractive to external resources and show stronger resilience in a volatile environment. Governments are expected to roll out appropriate regulations to minimize the financial costs of regulations compliance and, meanwhile, guarantee effectiveness. Hence, it is essential to study and understand how ETS affects the firm competitiveness in seven pilot projects. This study explores the firm competitiveness of participants in the power and heat production sector from the perspectives of firm profitability, production investment, and environmental performance. The data on Return-of-Assets (ROA), operating costs, and carbon emissions at the firm level have been collected from the China Stock Market & Accounting Research Database (CSMAR) and the Carbon Emission Accounts & Datasets (CEADs). The Difference-in-Differences (DID) method is employed for data analysis, and complete robustness tests are conducted to justify the validity of the study. The results indicate that implementing pilot ETS could increase firm profitability but reduce the production investment, and the environmental performance of the firms reveals that the pilot ETS has achieved emission reduction during the observation period without time lag. This study makes the following contributions to the current academic literature. First, it could serve as a micro-economic analysis of ETS impacts. Second, it compares different definitions of firm competitiveness and establishes a multi-dimensional measurement framework for analyzing the performance of high-carbon firms in the ETS. At the same time, the results may also help firms further understand the ETS regulations and build optimal strategies in the market. Finally, the study is also expected to support decision-making in regulation modification and stakeholder engagement in the future

Properties of bio-oil based fuel mixtures: biochar/bio-oil slurry fuels and glycerol/bio-oil fuel blends

This thesis reports the properties of bio-oil-based fuel mixtures. For bioslurry fuels, the interaction between biochar and bio-oil results in changes in fuel properties and the redistribution of inorganic species. For glycerol/methanol/bio-oil (GMB) fuel blends, the solubility and fuel properties are improved upon methanol addition but other impurities in crude glycerol worsen the solubility with limited impact on properties. It is also possible to integrate the GMB blends production into the biodiesel production process

Experimental Study on the Effectiveness of Extracurricular Football Training for Improving Primary Students Physical Fitness

The purpose of this study is to examine the effectiveness of after-school football training in improving the physical fitness of primary school students, so as to provide corresponding Suggestions for carrying out after-school football training in primary schools. A total of 72 students from the experimental primary school of Mouping district, Yantai city, Shandong province, participated in this experimental study, including 36 in the experimental group and 36 in the control group.The experiment was conducted for two semesters. During the experiment period, the experimental group conducted one-hour football training after school from Monday to Thursday afternoon every week, and two hours of football training on Saturday morning every week. The control group conducted sports teaching and extracurricular activities as usual without other intervention. Before and after the experiment, both the experimental group and the control group underwent physical fitness tests according to the physical fitness test standards of Chinese students, including lung capacity, 50-meter run, one-minute skipping rope, sitting forward flexor, and one-minute sit-ups. The test results were all converted to the 100-point system according to the scoring standards. Before the experiment, there was no significant difference between the experimental group and the control group in various physical fitness indicators (p \u3e 0.05). After the experiment, the lung capacity score (T = 3.108, p \u3c 0.05), the 50-meter run score (T = 6.593, p \u3c 0.05), the skipping score (T = 9.227, p \u3c 0.05), the sitting forward flexor score (T = 3.742, p \u3c 0.05), and the sit-up score (T = 5.210, p \u3c 0.05) of the experimental group were significantly higher than that of the control group. This study shows that the physical fitness of primary school students can be improved by football training in their spare time. It is suggested to carry out after-school football training activities in primary schools so as to effectively improve the physical fitness of pupils

A Kind of Non-associative Groupoids and Quasi Neutrosophic Extended Triplet Groupoids (QNET-Groupoids)

The various generalized associative laws can be considered as generalizations of traditional symmetry. Based on the theories of CA-groupoid, TA-groupoid and neutrosophic extended triplet (NET), this paper first proposes a new concept, which is type-2 cyclic associative groupoid (shortly by T2CA-groupoid), and gives some examples and basic properties. Furthermore, as a combination of neutrosophic extended triplet group (NETG) and T2CA groupoid, the notion of type-2 cyclic associative neutrosophic extended triplet groupoid (T2CA NET-groupoid) is introduced, and a decomposition theorem of T2CA-NET-groupoid is proved. Finally, as a generalization of neutrosophic extended triplet group (NETG), the concept of quasi neutrosophic extended triplet groupoid (QNET-groupoid) is introduced, and the relationships among T2CA-QNET-groupoid, T2CA-NET-groupoid and CA-NET-groupoid are discussed